INSTRUCTIONS - Submit the R file you use to make your calculations and graphs. Use only RStudio software to obtain the answers to the questions. R Markdown files are also accepted. Model with real and nominal variables Let the following model be a modified version of the model pcnom.R with inflation of prices and wages. pcfisc_eqs 1=YC+G. eq2 =YnY, eq 3=NY/ prod, eq4 4=Wxi_wW[1]+(1xi_w)t(w0+w1(exp(100(N/N_fe1))1)), eq 5=WnWP, eq 6=WBWnN, eq7 7 Profits - Yn- WB, eqB =UCnWB/Y, eq 9=Pxi_pP[1]+(1xi_p)(1+markup)Cn. eq10 =Pi(P/P[1]1). eq11 = YDn - WB + Profits + r[-1] * Bh[-1] - TX, eq12 = YD - YDn/ P, eq13=TX - theta * (WB + Profits + r[-1] * Bh[-1]). eq14 =VnVn[1]+ YDn- Cn, eq15 =VVn/P, eq16 = C - alpha1 * YD + alpha2 * V[-1] , eq 17=CnCP, eq 18=HhVnBh, eq19=Bh Vn * (lambda0+ lambda1* r - lambda2* (YDn/Vn )). eq20 =BsBs[1]+(Gn+r[1]Bs[1])(TX+r[1]Bcb[1]). eq21 =Gn(1fiscsw((1rhog)Gnbar+rhogGn[1])+ fiscsw ( Gnbar+e gn ), eq22 =GGn/P, eq23 =HsHs[1]+BcbBcb[1], eq24 =BcbBsBh, eq 25=r rbar, eq26=redundant HsHh, ) The final2023_codeR file which is at the bottom of the questions includes the code needed to simulate this model. You must copy this code in your answer document and simulate it completely to be able to answer this question. a) Which model parameter captures the degree of price rigidity? Which parameter captures the degree of wage rigidity? Does the model as calibrated contain: 1) price stickiness only, 2) wage rigidity only or 3) both price and wage rigidity? b) It is generally accepted that increasing productivity is essential to improving the quality of life. Using the function sfc _shock, simulate the impact of an increase in productivity (prod) of 1%. Use start =3 and end =100. Simulate the shock for 100 periods. Draw the evolution of the level of price (deviation in \% compared to the initial steady state). Use only the first 40 observations of the simulation to make the graph. c) On the same graph, plot (deviation in \% from the initial steady state), the evolution of the real wage, the nominal wage and the unit cost of production. Only use the first 40 observations of the simulation to make d) Considering what you found in b) and c). how do you explain the impact of increase in productivity on the price level? e) On the same graph, plot (as a \% deviation from the initial steady state), the evolution of real consumption and nominal consumption. Only use the first 40 observations of the simulation to make the graph. Based on this graph, is it true to say that the increased production contributes to improving the standard of living of households? Briefly explain your reasoning. Now suppose that the 1% increase in productivity occurs at the same time as a pandemic decimates the economy's labor force, such that N_fe, the level of full employment, falls simultaneously by 1.625%. f) Using the function sfer_shock, simulate the impact of the increase in productivity (prod) of 1% and the simultaneous drop in full employment ( N_fe ) of 1,625%. Usestart =3 and end =100. Simulate the shock for 100 periods. Trace the evolution of the price level (in \% deviation from the state initial stationary). On the same graph, also plot the evolution (in \% deviation compared to the initial steady state) of the price level coming from the simulation obtained in question b). Use only the first 40 observations of the simulation to make the graph. How do you explain the difference between the result obtained in f ) and the result obtained in b)? g) On the same graph, plot (as a \% deviation from the initial steady state), the evolution of real consumption and nominal consumption following the simulation carried out in f). Use only the first 40 observations from the simulation to make the graph. In your opinion, what would have happened to real consumption if, following the 1.625% fall in N_fe, we had NOT observed the increase in productivity of 1% Explain your reasoning intuitively V=V[1]+(YDC), C - alpha1 * YD+ alpha2 * v[1], Hh - V - Bh, BsBs[1]+(G+x[1]Bs[1])(T+x[1]Bcb[1]). Hs - Hs [1]+BcbBcb[1]. Bcb - Bs - Bh, redondant Hs - Hh ) Pc_exog I=0.025, G=20, alphal - 0.8, alpha2 - 0.2, theta * 0.2, 1 ambda 00.635, 1 ambda 1+5, lambda2 -0.01 ) * Simulate from seratch nper